Divide a decimal by a natural number

### 1.1. Knowledge to remember

**a)** __Example 1__: A rope 8.4m long is divided into 4 equal segments. How many meters long is each piece of string?

We have to do the division: 8.4 : 4 = ?

We have: 8.4 m = 84dm

So 8.4 : 4 = 2.1 (m)

Usually we set the calculation and then do the following:

- 8 divided by 4 get 2, write 2; 2 times 4 equals 8; 8 minus 8 equals 0, write 0
- Write the right sign to the right 2
- Lower 4; 4 divided by 4 get 1, write 1; 1 times 4 equals 4; 4 minus 4 equals 0, write 0

**b)** __Example 2__: 72.58 : 19 = ?

We set the calculation and then do the same as for example 1:

To divide a decimal by a natural number, do the following:

- Divide the integer part of the divisor by the divisor.
- Write a comma to the right of the quotient found before taking the first digit in the decimal part of the divided number to continue the division.
- Continue dividing with each digit in the decimal part of the number being divided.

### 1.2. Solving textbook exercises on page 64

**Lesson 1**

Calculate then calculate:

a) 5.28 : 4 ; b) 95.2 : 48

c) 0.36 : 9 d) 75.52 : 32.

__Solution guide:__

a) \(\begin{array}{l}

\left. \begin{array}{l}

5.28\\

1\,\,2

\end{array} \right|\begin{array}{*{20}{c}}

4\\

\hline

{1,32}

\end{array}\\

\,\,\,08\\

\,\,\,\,\,\,0

\end{array}\) b) \(\begin{array}{l}

\left. \begin{array}{l}

95.2\\

27\,\,2

\end{array} \right|\begin{array}{*{20}{c}}

4\\

\hline

{1,4}

\end{array}\\

\,\,\,0\,\,0

\end{array}\)

c) \(\begin{array}{l}

\left. \begin{array}{l}

0.36\\

0\,\,3

\end{array} \right|\begin{array}{*{20}{c}}

9\\

\hline

{0.04}

\end{array}\\

\,\,\,\,\,36\\

\begin{array}{*{20}{c}}

{}&0

\end{array}

\end{array}\) d) \(\begin{array}{l}

\left. \begin{array}{l}

75.52\\

11\,\,\,5

\end{array} \right|\begin{array}{*{20}{c}}

{32}\\

\hline

{2,36}

\end{array}\\

\,\,\,1\,\,92\\

\begin{array}{*{20}{c}}

{}&0

\end{array}

\end{array}\)

Lesson 2

Find x:

a) x × 3 = 8.4 b) 5 × x = 0.25

__Solution guide:__

a) x × 3 = 8.4x × 3 b) 5 × x = 0.25

x = 8.4 : 3 x = 0.25:5

x = 2.8 x = 0.05

lesson 3

A person riding a motorbike in 3 hours travels 126.54km. On average, how many kilometers does that person walk per hour?

__Solution guide:__

The average number of kilometers traveled per hour is :

126.54 : 3 = 42.18(km)

Answer: 42.18km.

### 1.3. Solve the exercises in the textbook Practice page 64

Lesson 1

Calculate then calculate:

a) 67.2 : 7 b) 3.44 : 4

c) 42.7 : 7 d) 46,827 : 9

__Solution guide:__

a) \(\begin{array}{*{20}{l}}

{\left. {\begin{array}{*{20}{l}}

{67,2}\\

{{\mkern 1mu} {\mkern 1mu} 4{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} 2}

\end{array}} \right|\begin{array}{*{20}{c}}

7\\

\hline

{9,6}

\end{array}}\\

{\begin{array}{*{20}{c}}

{}&0

\end{array}}

\end{array}\)

b)

\(\begin{array}{*{20}{l}}

{\left. {\begin{array}{*{20}{l}}

{47.2}\\

{{\mkern 1mu} {\mkern 1mu} 0{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} 7}

\end{array}} \right|\begin{array}{*{20}{c}}

7\\

\hline

{6,1}

\end{array}}\\

{\begin{array}{*{20}{c}}

{}&0

\end{array}}

\end{array}\)

c) \(\begin{array}{l}

\left. \begin{array}{l}

3.44\\

3\,\,4

\end{array} \right|\begin{array}{*{20}{c}}

7\\

\hline

{0.86}

\end{array}\\

\,\,\,\,\,24\\

\begin{array}{*{20}{c}}

{}&0

\end{array}

\end{array}\) d) \(\begin{array}{l}

\left. \begin{array}{l}

46,827\\

\,\,\,1\,\,\,8

\end{array} \right|\begin{array}{*{20}{c}}

9\\

\hline

{5,203}

\end{array}\\

\,\,\,\,\,\,\,027\\

\begin{array}{*{20}{c}}

{}&{\,\,\,\,\,0}

\end{array}

\end{array}\)

Lesson 2

a)

In this division, the quotient is 1.24 and the remainder is 0.12 .

Retry: 1.24 × 18 + 0.12 = 22.44

b) Find the remainder of the following division:

__Solution guide:__

b) Straightening the column of commas in the divisor down to the position of the remainder we get 0.14

So in this division, quotient is 2.05, remainder is 0.14

Retry: 2.05 × 21 + 0.14 = 43.19

lesson 3

Calculate then calculate:

a)26.5:25 b)12,24:20

Note: When dividing a decimal number by a natural number that has a remainder, we can continue to divide by: writing an additional 0 to the right of the remainder and then continuing to divide. Such as:

__Solution guide:__

\(\begin{array}{l}

\left. \begin{array}{l}

21.3\\

\,\,\,1\,\,\,3

\end{array} \right|\begin{array}{*{20}{c}}

5\\

\hline

{4,26}

\end{array}\\

\,\,\,\,\,\,\,30\\

\begin{array}{*{20}{c}}

{}&{\,\,\,\,\,0}

\end{array}\\

\left. {\begin{array}{*{20}{c}}

{26.5}&{}\\

{150}&{}

\end{array}} \right|\begin{array}{*{20}{c}}

{25}\\

\hline

{1.06}

\end{array}\\

\begin{array}{*{20}{c}}

{}&0

\end{array}

\end{array}\)

\(\begin{array}{l}

\left. {\begin{array}{*{20}{c}}

{12,24}&{}\\

{12\,2}&{}

\end{array}} \right|\begin{array}{*{20}{c}}

{20}\\

\hline

{0.612}

\end{array}\\

\begin{array}{*{20}{c}}

{}&{24}

\end{array}\\

\begin{array}{*{20}{c}}

{}&{\,\,\,40}

\end{array}\\

\begin{array}{*{20}{c}}

{}&{\begin{array}{*{20}{c}}

{}&0

\end{array}}

\end{array}

\end{array}\)

**Lesson 4**

There are 8 bags of rice weighing 243.2 kg. How many kilograms does 12 such bags of rice weigh?

__Solution guide:__

Each bag in kilograms is:

243.2 : 8 = 30.4(kg)

1212 bags weighing in kilograms are:

30.4 × 12 = 364.8(kg)

Answer: 364.8kg.

.

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